Congruent and Similar Shapes Worksheet

Lesson Overview

About this worksheet

Congruent and similar are two of the most-confused terms in elementary geometry, and the worksheet keeps the distinction simple: CONGRUENT means same shape AND same size (a sliding/flipping/turning copy); SIMILAR means same shape but DIFFERENT size (a scaled copy). Every congruent pair is also similar (the ratio is 1 to 1), but most similar pairs are NOT congruent. When two shapes have different SHAPES at all, they are neither congruent nor similar.

The reference box at the top of page 1 teaches the rule and the transformation hint (slide / flip / turn preserves congruence; resize preserves similarity but not congruence), then works through a single example: a square with side 3 inches and a square with side 6 inches are similar (same shape) but not congruent (sizes differ). The (3, 6) pair does NOT appear in any assessed item.

Section A on page 1 has 8 shape-pair items. Five items use rectangles or squares with explicit dimensions (5 vs 5, 4 vs 8, 6×4 vs 6×4, 4×6 vs 8×12, 4×6 vs 6×4) so students can compare numerically. Two items test edge cases: same-angle-different-side triangles are SIMILAR by the AA criterion (item 7), and a rotated rectangle (4×6 vs 6×4) is still CONGRUENT because rotation preserves size (item 6). One item is a NEITHER (circle vs triangle, item 3) so students cannot pattern-match. Section B on page 2 has 6 definition fill-ins.

Section C on page 2 has 3 reasoning word problems with work boxes (1.10in): two triangles with sides 5-12-13 (both congruent AND similar), a 4×6 photo enlarged to 8×12 (similar, ratio 1 to 2), and the famous ‘are all squares similar to each other’ question (yes – 4 right angles + 4 matching sides means the ratio is always fixed). Page 3 is a complete answer key.

How to Use This Lesson

Project the page-1 reference and read both definitions out loud: CONGRUENT = same shape AND same size; SIMILAR = same shape but DIFFERENT size.

Walk through the (3-inch square, 6-inch square) worked example; show that the ratio of sides is 1 to 2, which makes them similar but not congruent.

Work Section A item 1 (two squares, both side 5 cm) together; ask what changes when both squares have the SAME side length (congruent).

Walk through Section A item 6 (rectangle 4 by 6 and rectangle 6 by 4) since the rotation case is the most counter-intuitive (congruent, not just similar).

Assign the rest of Section A independently; remind students to check SAME SHAPE before checking SAME SIZE.

Read Section B item 13 (‘most similar shape pairs are not ____’) together; have students explain why the answer is CONGRUENT.

Use Section C item 17 (all squares are similar to each other) as a closing discussion to anchor the AA / matching-angles rule.

Use the answer key on page 3 for self-check or aide spot-check.

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